United were told on New Year's Day that they will be missing Pogba for the whole of January, and maybe longer after he picked an injury to his ankle which will require surgery, and with Scott McTominay also out with a knee injury, it means the club have had a rethink and may now enter the transfer market.
Pogba was sent for a scan after he reported pain in his ankle after the Boxing Day win over Newcastle and it confirmed he needed an operation.
McTominay has been told he will be out for two months, so the option now is to move into the transfer market this month and land a couple of players who could step in, but the Norwegian boss has made it clear he will not buy players for the sake of it.
"Of course it is playing on our decision-making when we have two players out - Paul for a month and Scott for two," Solskjaer said. "That will give us less options and we have loads of games and important games, but still it has to be right and that is the big point.
"If it's available and if it's possible we will do something, definitely. We are looking at one or two."
With the season entering a crucial period, United know they need to keep pace near the top of the Premier League if they are to have a chance of winning a coveted top-four spot.
However, they suffered a setback after losing at Arsenal on Wednesday.
United struggled to create chances and remain five points adrift of fourth-placed Chelsea.
Without Pogba, who continues to be linked with a move to Juventus, and McTominay at Arsenal, Nemanja Matic and Fred lined up together in the centre of the park.
The duo helped United to three points at Burnley but could not have the same effect at the Emirates.
Solskjaer added: "It is a big blow that Paul is out, now that Scott's out, because Scott will be out for a few months and that is a big blow for us. Scott has been magnificent.
"It is nothing major. It is something that has to be sorted and dealt with, within a time frame."